Quasi-periodic solutions for the forced Kirchhoff equation on \mathbbT^d

2018/02/08 by Livia Corsi, Riccardo Montalto
Mathematics · #math.AP #msc:37K55 #msc:35L72

paper · pdf · doi:10.1088/1361-6544/aad6fe

arXiv admin note: text overlap with arXiv:1311.6943

arxiv created 2018/02/08 · arxiv updated 2018/11/14

Abstract

In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the d-dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of this type for a quasi-linear equations in high dimension. The proof is based on a Nash-Moser scheme in Sobolev class and a regularization procedure combined with a multiscale analysis in order to solve the linearized problem at any approximate solution.

Citations

• An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifold